## PRP Records

### Probable Primes Top 10000

#### (292102 PRPs in the top)

What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!

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See the Latest PRPs
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 1-250 251-500 501-750 751-1000 1001-1250 1251-1500 1501-1750 1751-2000 2001-2250 2251-2500 2501-2750 2751-3000 3001-3250 3251-3500 3501-3750 3751-4000 4001-4250 4251-4500 4501-4750 4751-5000 5001-5250 5251-5500 5501-5750 5751-6000 6001-6250 6251-6500 6501-6750 6751-7000 7001-7250 7251-7500 7501-7750 7751-8000 8001-8250 8251-8500 8501-8750 8751-9000 9001-9250 9251-9500 9501-9750 9751-10000

 Rank Probable prime Digits (> 50000) Who ? When ? 6001 2^344309-1852033 103648 Enzo Doria 08/2015 6002 25729^10672+10672^25729 103643 Hans Havermann 09/2020 6003 (2^344289+1166)/2 103642 Stefano Morozzi 09/2020 6004 3*10^103637+61 103638 Robert Price 09/2020 6005 (2^344246+1614)/2 103629 Stefano Morozzi 09/2020 6006 2^344213-21253 103619 Enzo Doria 06/2013 6007 2^344196-465 103614 Lelio R Paula 11/2016 6008 2^344187-20001 103611 Enzo Doria 06/2013 6009 (117191#+(355573#)/(117191#))/(200233679) 103602 Makoto Morimoto 10/2017 6010 (237^43627-1)/236 103601 Serge Batalov 06/2022 6011 20^79621-19^79621 103590 Jean-Louis Charton 03/2011 6012 Phi(155391,10)/1243129 103586 Maksym Voznyy 09/2015 6013 2^344085-20365 103580 Enzo Doria 06/2013 6014 5^148169+54 103566 Lelio R Paula 11/2016 6015 2^344017-108795 103560 Enzo Doria 03/2014 6016 (2^343974+2670)/2 103547 Stefano Morozzi 09/2020 6017 2^343971-5077 103546 Lelio R Paula 09/2011 6018 (7*10^103531+71)/3 103532 Robert Price 05/2018 6019 2^343899+141 103524 Lelio R Paula 08/2011 6020 (2^343933+1)/(3*98294339989393) 103520 Gord Palameta 08/2018 6021 6^133029-67 103517 Lelio R Paula 11/2016 6022 (17*2^343877+1)/13625 103515 Lelio R Paula 12/2013 6023 66*10^103507+7 103509 Robert Price 07/2020 6024 26297^8614+8614^26297 103485 Hans Havermann 09/2020 6025 (2^343764+2658)/2 103483 Stefano Morozzi 09/2020 6026 26499^8036+8036^26499 103480 Hans Havermann 09/2020 6027 (136*10^103474-1)/9 103476 Serge Batalov 12/2014 6028 5^148014-24 103458 Lelio R Paula 11/2016 6029 28316^4503+4503^28316 103453 Hans Havermann 09/2020 6030 (22*10^103450+53)/3 103451 Robert Price 07/2019 6031 2^343604+9931 103436 Yves Minet 01/2011 6032 2^343601-21189 103435 Enzo Doria 06/2013 6033 (10^103423+173)/3 103423 Robert Price 05/2021 6034 2^343508-115229 103407 Enzo Doria 06/2015 6035 (8766^26227-1)/8765 103404 Serge Batalov 06/2022 6036 (509203*2^343491-1)/16147 103403 Lelio R Paula 05/2015 6037 3^216685-113056 103386 Enzo Doria 07/2014 6038 24829^14580+14580^24829 103382 Hans Havermann 08/2020 6039 91355!4+1024 103381 Robert Price 09/2019 6040 44^62903-43^62903 103379 Jean-Louis Charton 08/2012 6041 11^99262-20 103371 Lelio R Paula 12/2016 6042 (509203*2^343357-1)/5 103366 Lelio R Paula 05/2015 6043 (2^343363+3570)/2 103363 Stefano Morozzi 09/2020 6044 2^343356-2791889 103361 Enzo Doria 03/2016 6045 (25*10^103360-241)/9 103361 Robert Price 05/2018 6046 Phi(104989,10)/2939693 103350 Maksym Voznyy 09/2015 6047 24826^14511+14511^24826 103319 Hans Havermann 09/2020 6048 2^343182-171 103309 Lelio R Paula 08/2011 6049 (23619^23619+23620^23620)/7187 103294 David Broadhurst 09/2009 6050 (10680^25639-1)/10679 103285 Serge Batalov 06/2022 6051 (7427^26683-1)/7426 103282 Serge Batalov 06/2022 6052 2^343079-1835611 103278 Enzo Doria 05/2015 6053 2^343063-1147 103273 Yves Minet 06/2013 6054 24741^14930+14930^24741 103271 Hans Havermann 09/2020 6055 (16*10^103255-73)/3 103256 Robert Price 07/2020 6056 (219^44119-1)/218 103256 Serge Batalov 06/2022 6057 9*6^132689+7 103254 Lelio R Paula 11/2014 6058 2^342979-18085 103247 Enzo Doria 05/2013 6059 (16*10^103244-31)/3 103245 Robert Price 03/2019 6060 2^342966-16995 103244 Lelio R Paula 11/2016 6061 23797^21774+21774^23797 103230 Hans Havermann 09/2020 6062 25388^11637+11637^25388 103224 Hans Havermann 09/2020 6063 (2^342876+2086)/2 103216 Stefano Morozzi 09/2020 6064 (16*10^103214-31)/3 103215 Robert Price 03/2019 6066 (37*10^103211+611)/9 103212 Robert Price 11/2018 6065 (238*10^103210-1)/3 103212 Robert Price 04/2020 6067 5^147650+16 103203 Lelio R Paula 11/2016 6068 gcd(Phi(852060,10),(10^42603+1)^3*(10^42603+1-10^21302)+(10^85206+10^42603)*(10^21302+1)+10^127809) 103201 Serge Batalov 04/2015 6069 2^342817+2707067 103199 Enzo Doria 03/2016 6070 43^63177-42 103198 Theodore Burton 02/2007 6071 2^342805-21025 103195 Enzo Doria 06/2013 6072 24129^18890+18890^24129 103182 Hans Havermann 09/2020 6073 (622*10^103171-1)/9 103173 Robert Price 11/2021 6074 2^342714+12285 103168 Lelio R Paula 11/2016 6075 (2*10^103161-17)/3 103161 Serge Batalov 11/2022 6076 18^82178-4481 103156 Enzo Doria 03/2013 6077 2^342665-17349 103153 Enzo Doria 05/2013 6078 30408^2467+2467^30408 103150 Hans Havermann 09/2020 6079 (5^147571-3^147571)/2 103148 Kellen Shenton 05/2022 6080 (2^342615+3090)/2 103138 Stefano Morozzi 09/2020 6081 2^342612+175 103137 Lelio R Paula 08/2011 6082 5*2^342585-3 103130 Lelio R Paula 09/2014 6083 (16*10^103127+77)/3 103128 Robert Price 03/2019 6084 (2^342527+3774)/2 103111 Stefano Morozzi 02/2021 6085 2^342503-19209 103104 Enzo Doria 05/2013 6086 (2^342484+2586)/2 103098 Stefano Morozzi 09/2020 6087 2^342476+51 103096 Lelio R Paula 08/2011 6088 2^342460-18885 103091 Enzo Doria 05/2013 6089 (2^342442+862)/2 103086 Stefano Morozzi 02/2021 6090 (194*10^103074-17)/3 103076 Robert Price 09/2020 6091 7^121968+82 103075 Lelio R Paula 10/2016 6092 2^342392-108863 103071 Enzo Doria 03/2014 6093 (2^342389+806)/2 103070 Stefano Morozzi 01/2021 6094 3^216014+28 103065 Lelio R Paula 11/2016 6095 2^342353-108879 103059 Enzo Doria 03/2014 6096 10^103055+276081 103056 Patrick De Geest 12/2016 6097 10^103055-53 103055 Lelio R Paula 11/2016 6098 (58*10^103046+419)/9 103047 Robert Price 05/2019 6099 7^121933+4 103046 Lelio R Paula 11/2014 6100 (71*10^103028-143)/9 103029 Robert Price 10/2021 6101 (2^342235+3618)/2 103023 Stefano Morozzi 09/2020 6102 19^80560-68 103017 Lelio R Paula 10/2016 6103 2^342209+76607 103016 Enzo Doria 05/2016 6105 328^40945+40945^328 103013 Norbert Schneider 12/2014 6104 12^95454-91 103013 Lelio R Paula 10/2016 6106 25833^9716+9716^25833 103009 Hans Havermann 01/2019 6107 (893*10^103004+7)/9 103006 Robert Price 06/2021 6108 (1475^32503-1)/1474 102993 Serge Batalov 06/2022 6109 65^56809-64^56809 102990 Robert Price 08/2013 6110 5^147338-6 102985 Lelio R Paula 11/2014 6111 2^342084-112739 102978 Enzo Doria 06/2014 6112 9*6^132330+7 102974 Lelio R Paula 11/2014 6113 2^342034-16737 102963 Enzo Doria 05/2013 6114 (9787*2^342011-1)/25 102959 Lelio R Paula 05/2015 6115 (3^215802-5)/124343756 102956 Lelio R Paula 12/2013 6116 2^341991-17421 102950 Enzo Doria 05/2013 6117 2^341969-112225 102943 Enzo Doria 06/2014 6118 (9787*2^341864-1)/3 102915 Lelio R Paula 05/2015 6119 2^341859+1869413 102910 Enzo Doria 05/2016 6120 10^102909+61 102910 Lelio R Paula 11/2016 6121 10^102909-67049 102909 Patrick De Geest 12/2016 6122 23814^20935+20935^23814 102898 Hans Havermann 02/2019 6123 28345^4264+4264^28345 102888 Hans Havermann 02/2019 6124 25665^10204+10204^25665 102886 Hans Havermann 02/2019 6125 26288^8181+8181^26288 102860 Hans Havermann 02/2019 6126 2^341659+1836773 102850 Enzo Doria 03/2016 6127 2^341608-110639 102835 Enzo Doria 05/2014 6128 10^102824+49 102825 Lelio R Paula 11/2016 6129 10^102824-168011 102824 Patrick De Geest 12/2016 6130 11^98708-8 102794 Lelio R Paula 10/2016 6131 2^341466+4429 102792 Lelio R Paula 09/2011 6132 2^341460-107 102790 Lelio R Paula 08/2011 6133 (2^341388+47)/21014943 102761 Lelio R Paula 12/2013 6134 2^341355+21 102759 Lelio R Paula 08/2011 6135 (6496^26947-1)/6495 102736 Serge Batalov 06/2022 6136 2^341246+40755 102726 Lelio R Paula 11/2016 6137 (2^341256-5)/991699 102723 Lelio R Paula 12/2013 6138 7^121547+78 102720 Lelio R Paula 10/2016 6139 2^341223-461197 102719 Enzo Doria 06/2015 6140 27838^4893+4893^27838 102711 Hans Havermann 03/2019 6142 2^341190-20577 102709 Enzo Doria 06/2013 6141 (27*2^341212+1)/84674449 102709 Lelio R Paula 12/2013 6143 (25*10^102698+77)/3 102699 Robert Price 09/2022 6144 6^131976-65 102698 Lelio R Paula 10/2016 6145 2^341134+2533 102692 Henri Lifchitz 09/2005 6146 13^92184-54 102688 Lelio R Paula 10/2016 6147 2^341116-20873 102687 Enzo Doria 06/2013 6148 2^341094-19953 102680 Enzo Doria 06/2013 6149 23761^20950+20950^23761 102676 Hans Havermann 03/2019 6151 2^341053+129 102668 Lelio R Paula 08/2011 6150 (4724^27943-1)/4723 102668 Serge Batalov 06/2022 6153 (31*2^341006-1)/3 102655 Lelio R Paula 03/2014 6152 7^121471+94 102655 Lelio R Paula 10/2016 6155 2^341004-173 102653 Lelio R Paula 08/2011 6154 20^78901+3 102653 Lelio R Paula 10/2016 6156 (2^341001+1674)/2 102652 Stefano Morozzi 09/2020 6157 5^146853-52 102646 Lelio R Paula 10/2016 6158 2^340969-216931 102642 Enzo Doria 05/2014 6159 122^49196+121 102641 Norbert Schneider 10/2018 6160 2^340952+1870021 102637 Enzo Doria 05/2016 6161 5*2^340940-3 102634 Lelio R Paula 08/2014 6162 (6^131891+1)/7 102631 Paul Bourdelais 01/2010 6163 (11*10^102629-23)/3 102630 Robert Price 09/2021 6164 25876^9239+9239^25876 102615 Hans Havermann 02/2019 6165 (4*10^102612+83)/3 102613 Robert Price 02/2018 6166 75^54717+74 102598 Norbert Schneider 01/2015 6167 (17*10^102597+13)/3 102598 Robert Price 01/2019 6168 2^340806-20393 102593 Enzo Doria 06/2013 6169 (2^340790+5)/138267 102583 Lelio R Paula 12/2013 6170 6^131821+77 102577 Lelio R Paula 10/2016 6171 (203*10^102561-11)/3 102563 Robert Price 12/2020 6172 2^340688-29 102558 Henri Lifchitz 05/2005 6173 2^340685-109101 102557 Enzo Doria 04/2014 6174 65^56567-64 102552 Norbert Schneider 11/2014 6175 26230^8121+8121^26230 102550 Hans Havermann 03/2019 6176 (64*10^102547+161)/9 102548 Robert Price 08/2022 6177 (8*10^102541+49)/3 102542 Robert Price 05/2020 6178 (536*10^102533-23)/9 102535 Robert Price 02/2020 6179 2^340547-108897 102515 Enzo Doria 03/2014 6180 (2^340536+778)/2 102512 Stefano Morozzi 09/2020 6181 25592^10119+10119^25592 102500 Hans Havermann 02/2019 6182 (5*10^102492-23)/9 102492 Serge Batalov 11/2022 6183 7^121268+82 102484 Lelio R Paula 10/2016 6184 (6883*2^340443-1)/162401 102483 Lelio R Paula 05/2015 6185 2^340434-5955 102481 Lelio R Paula 11/2016 6186 (7*10^102480-19)/3 102481 Robert Price 10/2020 6187 (2^340381+47)/7 102465 Lelio R Paula 12/2013 6188 111^50095+110 102461 Norbert Schneider 04/2017 6189 2^340291-20301 102438 Enzo Doria 06/2013 6190 12^94915+89 102431 Lelio R Paula 10/2016 6191 (106*10^102422+17)/3 102424 Robert Price 04/2021 6192 24466^15349+15349^24466 102417 Hans Havermann 03/2019 6193 2^340212+111546435 102415 Paul Bourdelais 10/2021 6194 2^340208-20373 102413 Enzo Doria 06/2013 6195 6^131598-17273 102404 Enzo Doria 02/2013 6196 (2^340132+1182)/2 102390 Stefano Morozzi 09/2020 6197 (2^340133+1166)/2 102390 Stefano Morozzi 09/2020 6198 2^340115-21181 102385 Enzo Doria 06/2013 6199 (55459*2^340090+1)/1591 102379 Lelio R Paula 07/2014 6200 (2^340064+3630)/2 102370 Stefano Morozzi 09/2020 6201 89^52511-88^52511 102365 Robert Price 06/2015 6202 3^214539-112756 102362 Enzo Doria 07/2014 6203 23159^23450-23450^23159 102353 Norbert Schneider 12/2019 6204 2^340000-19877 102351 Enzo Doria 06/2013 6205 2^339990-114845 102348 Enzo Doria 05/2015 6206 (3^214516-2)/51383 102346 Lelio R Paula 12/2013 6207 20^78661-99 102341 Lelio R Paula 09/2016 6208 2^339951-19585 102336 Enzo Doria 05/2013 6209 (17*10^102335-167)/3 102336 Robert Price 05/2022 6210 (13*2^339943+1)/45 102333 Lelio R Paula 12/2013 6211 (236282#+121441)/(121441*25499429) 102332 Makoto Morimoto 08/2020 6212 5*10^102323-91 102324 Robert Price 03/2021 6214 2^339889+29327 102317 Yves Minet 06/2010 6213 (167*10^102315-17)/3 102317 Robert Price 03/2020 6215 26348^7641+7641^26348 102314 Hans Havermann 03/2019 6216 Phi(239414,10)/6333218543 102303 Makoto Kamada 08/2019 6217 2^339834-109493 102301 Enzo Doria 04/2014 6218 (16*10^102299-19)/3 102300 Robert Price 02/2019 6219 (11^98221-5^98221)/6 102286 Robert Price 01/2013 6220 3^214365+1820 102279 Lelio R Paula 10/2016 6221 31978^1579+1579^31978 102278 Hans Havermann 03/2019 6222 (89*10^102262-467)/9 102263 Robert Price 04/2022 6223 (11*2^339705-1)/183 102261 Lelio R Paula 03/2014 6224 2^339694-16995 102259 Lelio R Paula 09/2016 6225 (56*10^102255+691)/9 102256 Robert Price 05/2019 6226 122^49008+121 102249 Norbert Schneider 10/2018 6227 (2^339652+3178)/2 102246 Stefano Morozzi 09/2020 6228 7^120985-38 102245 Lelio R Paula 10/2016 6229 10^102244+122961 102245 Patrick De Geest 12/2016 6230 10^102244-27 102244 Lelio R Paula 09/2016 6231 7^120982-62 102242 Lelio R Paula 10/2016 6232 (2^339640+2670)/2 102242 Stefano Morozzi 09/2020 6233 4*6^131382-5 102236 Lelio R Paula 11/2014 6234 (2^339607+3290)/2 102232 Stefano Morozzi 02/2021 6235 2^339586-1091 102226 Yves Minet 11/2012 6236 11^98161-3072000 102225 Enzo Doria 12/2012 6237 9*7^120961-4 102225 Lelio R Paula 11/2014 6238 5*3^214250+2 102224 Serge Batalov 10/2010 6239 12^94713-59 102213 Lelio R Paula 10/2016 6240 12^94705+89 102204 Lelio R Paula 10/2016 6241 2^339407-177 102172 Lelio R Paula 08/2011 6242 4*10^102163-57 102164 Robert Price 10/2018 6243 2^339355+65 102157 Lelio R Paula 07/2011 6244 (28*10^102142-31)/3 102143 Robert Price 12/2019 6245 (2^339323+47)/880715 102141 Lelio R Paula 12/2013 6246 (2^339268+1758)/2 102130 Stefano Morozzi 09/2020 6247 s(178551) 102122 Robert Price 05/2020 6248 (797*10^102112-23)/9 102114 Robert Price 01/2022 6249 (5*10^102107+7)/3 102108 Tyler Busby 02/2023 6250 (2^339175+2790)/2 102102 Stefano Morozzi 02/2021

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 20 2023 09:01 (Time in France)

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